B M Sharma Solutions for Chapter: Electromagnetic Induction, Exercise 2: DPP

A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is $n$ and the cross-sectional area of the coil is $A$. When the coil turns through $180°$ about its diameter, the charge flowing through the coil is $Q$. The total resistance of the circuit is $R$. What is the magnitude of the magnetic induction?

A hundred turns of insulated copper wire are wrapped around an iron cylinder of area $1\times {10}^{-3} {\mathrm{m}}^2$ and are connected to a resistor. The total resistance in the circuit is $10 \mathrm{ohms}$. If the longitudinal magnetic induction in the iron changes from $1 \mathrm{weber} {\mathrm{m}}^{-2}$ in one direction to $1 \mathrm{weber} {\mathrm{m}}^{-2}$ in the opposite direction, how much charge will flow through the circuit?

The magnetic flux is changed through a coil of resistance $10 \mathrm{ohm}$. As a result, an induced current is developed in it which varies with time as shown in figure. The magnitude of change in flux through the coil in weber is,

The magnetic field in the cylindrical region, shown in the figure, increases at a constant rate of $20 \mathrm{mT} {\mathrm{s}}^{-1}$. Each side of the square loop $ABCD$ has a length of $1 \mathrm{cm}$ and resistance of $4 \mathrm{\Omega }$. Find the current in the wire $AB$, if the switch $S$ is closed.

In the graph, variation of magnetic field with time $t$, applied perpendicular to the plane of the ring, is shown. Choose the correct statement.

A conducting loop rotates with constant angular velocity about its fixed diameter in a uniform magnetic field whose direction is perpendicular to the fixed diameter.
 

A plane rectangular loop is placed in a magnetic field. The emf induced in the loop due to this field is ${\epsilon }_i$ whose maximum value is ${\epsilon }_{im}$. The loop was pulled out of the magnetic field at a variable velocity. Assume that $\overrightarrow{B}$ is uniform and constant. ${\epsilon }_i$ is plotted against time $t$ as shown in the graph. Which of the following is/are correct?

A triangular loop, as shown in the figure, is being pulled out at $t=0$ from a uniform magnetic field with a constant velocity $v.$ The total resistance of the loop is constant and is equal to $R$. Then, the variation of power produced in the loop with time will be,